Strong Field Dynamics of Bosonic Fields

Strong field dynamics of bosonic fields: Looking for new particles and modified gravity

William East, Perimeter Institute ICERM Workshop October 26, 2020 ... Introduction

How can we use gravitational waves to look for new matter? Can we come up with alternative predictions for black holes and/or GR to test against observations? Need understanding of relativistic/nonlinear dynamics for maximum return

William East Strong field dynamics of bosonic fields ... Three examples with bosonic fields

Black hole superradiance, boson stars, and modiﬁed gravity with non-minially coupled scalar ﬁelds

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Gravitational wave probe of new particles

Search new part of parameter space: ultralight particles weakly coupled to standard model

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Superradiant instability: realizing the black hole bomb

Massive bosons (scalar and vector) can form bound states, when frequency ω < mΩH grow exponentially in time. Search for new ultralight bosonic particles (axions, dark massive “photons," etc.) with Compton wavelength comparable to black hole radius (Arvanitaki et al.)

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Boson clouds emit gravitational waves

WE (2018)

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Boson clouds emit gravitational waves

50 100 500 1000 5000 104 107 Can do targeted 105 1000 searches–e.g. follow-up 10 0.100 black hole merger events, 0.001 1 or “blind" searches 0.8 0.6 Look for either resolved or 0.4 1 stochastic sources with 0.98 0.96 LIGO (Baryakthar+ 2017; 0.94 Zhu+ 2020; Brito+ 2017; 10-12 10-11 10-10 Tsukada+ 2019)

Siemonsen & WE (2020)

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Stochastic gravitational wave background

Can already place constraints on vector bosons with LIGO O1+O2 (with moderate assumptions on black hole spin)

Tsukada, Brito, WE, & Siemonsen (in prep.)

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Testing the black hole paradigm

Black hole seems to ﬁt. . . But are there horizonless objects that can give similar behavior?

Caltech/MIT/LIGO Lab

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Boson stars

Are easy to evolve (c.f. gravastars, constant density stars, etc.). Can be ultracompact. Can be rapidly spinning. Can have stable photon orbits, ergospheres, etc. But are they stable? 101 0.4 101 0.3 0 2 10 −

µM 0.2 M/R Repulsive JM Mini KKLS 100 0.1 1 Solitonic 10− Axionic 0.0 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 ω/µ ω/µ ω/µ

Siemonsen & WE (in prep.) William East Strong ﬁeld dynamics of bosonic ﬁelds ... Rotating boson star stability

Maybe not. . .

Palenzuela et al. (2017)

Also Sanchis-Gual et al. (2019): Rotating stars are unstable for massive scalar bosons; Rotating massive vector stars are more stable. (See J. Font’s talk)

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Boson stars

Use 3D full GR evolutions to study stability of complex scalar 0 0 boson stars with nonlinear interactions, Φ = V (Φ) with V nonlinear. 3.0 Repulsive 2.5 Mass Term KKLS 2.0 Solitonic 2

/µ Axionic (40 ) )

| × 1.5 Φ | (

V 1.0

0.5

0.0 0.00 0.25 0.50 0.75 1.00 1.25 1.50 Φ | |

Nils Siemonsen & WE (in prep.)

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Non-axisymmetric instability

Example of rotating axionic boson star

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Unstable and stable boson stars

1 10− KKLS Solitonic

I Axionic ˜ ω

M 2 10−

0.4 0.5 0.6 0.7 0.8

1 10− R ˜ ω M

2 10− 0.4 0.5 0.6 0.7 0.8 ω/µ

With nonlinear coupling, instability shuts off in relativistic regime for some cases.

Siemonsen & WE (in prep.)

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Boson stars: outlook

1 KKLS 10− Solitonic Axionic Repulsive 4 10− m Mini Φ

7 10−

0 2000 4000 6000 8000 10000 12000 t/M

Siemonsen & WE (in prep.)

Class of rotating scalar boson stars stable on long timescales Can study mergers of these as point of comparison to black holes. Longer timescale instabilities (e.g. ergoregion, light ring, etc.)?

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Modifying general relativity

1 Z 1 1 S = d 4x√ g( R ( φ)2 V (φ) + α (φ)( φ)4 + β (φ) 8π − 2 − 2 ∇ − ∇ G ∗ abcd abcd 2 6 + γ (φ) R Rabcd + (R Rabcd ) /Λ + ...)

Some modiﬁcations no longer have 2nd order equations of motion In that case one has no choice but to use order-reduction (see M. Okounkova’s talk) or modify short wavelength behavior (e.g. Cayuso & Lehner, 2020) For those with 2nd order equations (Horndeski theories) may be well-posed, but usually aren’t in commonly used formulations (Papallo & Reall).

William East Strong field dynamics of bosonic fields ... Modification to generalized harmonic — Kovacs & Reall (2020)

Introduce auxiliary metrics that determine gauge and constraint propagation.

Equations of motion will still be strongly hyperbolic for Horndeski theories with λ L2.

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Non-perturbative dynamics of Horndeski

Can we get this to work strong-ﬁeld/dynamical systems (e.g. black hole mergers) and non-negligible coupling? (Work with Justin Ripley) Focus on Einstein-dilaton Gauss Bonnet 1 Z 1 1 S = d 4x√ g R ( φ)2 + λφ 8π − 2 − 2 ∇ G

Representative example of Horndeski, violates null convergence condition Can leverage experience regarding hyperbolicity in spherically symmetric case (Ripley & Pretorius) See also Helvi Witek’s talk in previous workshop for test ﬁeld case.

William East Strong field dynamics of bosonic fields ... EDGB equations in modified harmonic

Evolution variables g , ∂t g , φ, ∂t φ { ab ab } ! A ef B g F (g) ab ab ∂2 ef + ab = 0 Cef D t φ F (φ)

with gauge choices Ha, g˜ , gˆ . { ab ab} In modiﬁed harmonic formulation, principal matrix no ef longer diagonal. In Horndeski, C and Bab non-zero, and matrix involves second-derivatives. Carry over experience with constraint damping, gauge conditions, from generalized harmonic. Black hole excision essential.

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Improved hyperbolicity

Harmonic vs. auxiliary metric harmonic

2.0 2.0 || h/L = 1/128 h/L = 1/1024 || h/L = 1/128 h/L = 1/1024 h/L = 1/256 h/L = 1/2048 h/L = 1/256 h/L = 1/2048 = 0) = 0)

t 1.5 h/L = 1/512 t 1.5 h/L = 1/512 ( ( h h ab ab g g 0 0

∂ 2 ∂ 2 || λ/L = 0.025 || λ/L = 0.025

/ 1.0 / 1.0

|| ˜ ˆ || ˜ ˆ

) A = 0.0, A = 0.0 ) A = 0.2, A = 0.4 t t ( ( h h ab ab g g

0 0.5 0 0.5 ∂ ∂ || ||

0.0 0.0 0 1 2 3 4 5 0 1 2 3 4 5 t/L t/L

Use of auxiliary metrics removes frequency dependence growth.

WE & Ripley in prep.

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Black hole collisions

0.5 1.04 2 2 λ/m2 = 0.05 λ/m = 0.00 λ/m = 0.15 λ/m2 = 0.05 λ/m2 = 0.18 0.4 2 1.02 λ/m = 0.10 λ/m2 = 0.10 λ/m2 = 0.15 0.3 1.00 2 /M

AH λ/m = 0.18 i AH φ h 0.2 M 0.98 Σ

0.1 0.96

0.0 0.94 0 50 100 150 200 250 300 350 0 50 100 150 200 250 t/M t/M

Black holes scalarize while shrinking, and then collide.

WE & Ripley in prep.

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Black hole collisions: radiation

4 4 10 10− 1.2 × − 1.0 × λ/m2 = 0.05 λ/m2 = 0.00 1.0 λ/m2 = 0.10 0.8 λ/m2 = 0.05 λ/m2 = 0.15 λ/m2 = 0.10 2

) 0.8 2 λ/m2 = 0.18 λ/m2 = 0.15 18

. 0.6

0 2 λ/m λ/m = 0.18 ( 0.6 GW P × 0.4 SF

˙ 0.4 E 0.2 0.2

0.0 0.0 160 170 180 190 200 210 220 230 160 170 180 190 200 210 220 230 (t r)/M (t r)/M − −

Scalar and gravitational wave radiation in full EDGB.

WE & Ripley in prep.

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Binary black hole inspiral

To do: Determine domain where theories are well-posed, and can give predictions for GW observations (case-by-case). Compare to order-reduction, other approximations that may not capture secular/non-perturbative effects.

William East Strong ﬁeld dynamics of bosonic ﬁelds ... Conclusion

Gravitational waves provide new probes of fundamental physics that may be inaccessible to terrestrial experiments.

Place interesting constraints on new particles with current, upcoming observations Can use boson stars to test limits of horizonless compact objects Make non-perturbative predictions for modiﬁed gravity theories (and determine where this is possible) Understanding of detailed dynamics, targeted analyses important.

William East Strong ﬁeld dynamics of bosonic ﬁelds